A Note on Unsteady Hydromagnetic Flow in a Rotating Channel Permeated by an Inclined Magnetic Field in the Presence of an Oscillator. Corrigendum and Addendum to Paper: Czech. J. Phys. 47 (1997), No. 8, pp. 787-792

Author has extended the literature on the topic as cited above which proliferates the theory of "Supercritical State", subject to plasma fusion in the interior state of the Sun. The co-existence of a modified restoring force and the Ghosh inertial frequency plays an important role in determining the interior state of the MHD flow field. This synchronization maintains the secrecy of the MHD flow field in a rotating environment when a forced oscillation is taken into account.     

Two-dimensional steady MHD flows in a nearly hyperbolic magnetic field

A solution for two-dimensional steady MHD flows in a nearly hyperbolic magnetic field is given. This solution exhibits the existence of a rectangular hyperbolic flow in the resistive region near the magnetic neutral point and is confirmed by recent laboratory experiments.     

Calculations of the parameters of the air plasma produced by an electron beam in the channel of an MHD generator with a nonequilibrium conductivity

Approximate analytic expressions for calculating the electron density in both steady and unsteady plasmas produced by pulsed electron beams are derived and proved to agree well with numerical calculations. It is shown that the algorithm for calculating the parameters of a nonequilibrium plasma in the channel of an MHD plasma generator depends on the type of generator. The effect of the magnetic field strength on the electron density and electric conductivity of the air plasma produced by an electron beam in the channel of a Faraday MHD generator is investigated. The influence of the parameters of the flow and ionizer on the efficiency of an MHD generator with a nonequilibrium conductivity is analyzed.     

弱磁场对Zn分枝状电解沉积物形貌的影响

用金相显微镜和原子力显微镜分析了存在外加磁场情况下的Zn分枝状电解沉积物的微观形貌 ，并且根据实验结果提出了磁场使沉积物分枝呈现螺旋状偏转的机理.1)在沉积物晶粒的早 期生长阶段，当晶粒已经形成了择优生长方向但又非常小,仍然悬浮于电解液中时，磁流体 动力学对流作用于它上面的不平衡力使得晶粒连同它的择优生长方向向着对流下方偏转，直 到晶粒足够大，和它的前一个单晶枝晶连接在一起为止.2)当晶粒和它的前一个单晶枝晶连 接在一起以后，磁流体动力学对流的作用力已不足使它偏转.此时，如果电解液的浓度比较 高，单晶枝晶的一级分枝和二级分枝之间不存在对电解质的竞争关系，则此单晶枝晶将完全 按照初期形成的晶体择优生长方向直线生长，直到新的晶粒形核为止;如果电解液浓度较低 ，造成第一级分枝与第二级分枝的竞争关系，二级分枝总在第一级分枝的上游侧生长，使得 一级分枝向下游方向偏转.通过上述两个步骤，无论是枝晶沉积物还是分形沉积物都产生螺 旋状偏转. 关键词： 电解沉积 磁流体动力学对流 晶体择优生长方向 生长形态     

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic(MHD) steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.     

Calculation of the electric potential and Lorentz force acting on a locally ionized region in a magnetohydrodynamic flow placed in a nonuniform magnetic field

An analytical solution to electrodynamic equations for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow in the nonuniform magnetic field produced by a straight-line conductor is found. Analytical formulas are obtained to evaluate the volume density of the Lorentz force and the integral Lorentz force acting on the locally ionized region of the MHD flow. It is shown that the MHD action on the locally ionized flow in the nonuniform magnetic field can be used to control the elevating force as well as the ratio of the elevating force to the drag force.     

高超声速飞行器磁控热防护系统建模分析

针对高超声速飞行器防热, 搭建了螺线管磁控热防护系统的物理模型. 采用低磁雷诺数磁流体数学模型, 分析了外加磁场强度及磁场形态对磁控热防护效果的影响. 对比了三种磁场类型(磁偶极子、螺线管、均布磁场)下磁控热防护效果的差异, 分析了螺线管几何参数对磁控热防护效果的影响. 研究表明, 磁场降低表面热流作用存在“饱和现象”; 三种磁场形态的磁控热防护能力从小到大依次为磁偶极子、螺线管、均布磁场; 相同驻点磁感应强度条件下, 增大螺线管半径有利于提高磁控热防护效果, 缩短螺线管与驻点距离不利于驻点和肩部防热, 螺线管长度对磁控热防护效果影响相对较小.     

Steady hydromagnetic flow between two porous concentric circular cylinders

The problem considered here is to study the MHD effects on the steady flow of an incompressibe viscous conducting fluid through two concentric porous non-conducting infinite circular cylinders, rotating in various ways with uniform angular velocities in presence of a radial magnetic field. It is supposed that the rate of suction at the inner cylinder is equal to the rate of injection at the outer.     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.     

Biomagnetic fluid flow in a channel with stenosis

In this study, the fundamental problem of the biomagnetic (blood) fluid flow in a channel with stenosis under the influence of a steady localized magnetic field is studied. The mathematical model used for the formulation of the problem is consistent with the principles of ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD). Blood is considered as a homogeneous Newtonian fluid and is treated as an electrically conducting magnetic fluid which also exhibits magnetization. For the numerical solution of the problem, which is described by a coupled, non-linear system of PDEs, with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by the development of an efficient pseudotransient numerical methodology using finite differences. This methodology is based on the development of a semi-implicit numerical technique, transformations and stretching of the grid and proper construction of the boundary conditions for the vorticity. Results concerning the velocity and temperature field, skin friction and rate of heat transfer indicate that the presence of the magnetic field influences the flow field considerably.     

水平磁场中液态锂膜流动实验装置及初步结果

设计了用于水平磁场中锂膜流动铺展性及磁流体动力学效应研究的实验装置，介绍了所用磁铁、锂循环回路、动力系统、回路温控系统和测量系统五个组成部分。各部分加工完成，进行现场组装与回路调试，最后加入锂锭熔融后完成实验台搭建工作。利用该实验台研究了锂膜在不锈钢表面的铺展情况、锂膜表面形态与流动雷诺数的关系，以及磁场对液膜表面形态的影响等方面。结果发现液态锂膜在充分锂浸润的不锈钢表面能够完全铺展，水平磁场对锂膜流动有致稳作用，并且可以抑制磁场方向的表面波动。     

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An experimental station, consisting of the magnet, the lithium flow loop, the dynamical circulation system, the heating system and the measure system, has been designed to study the liquid lithium film flow under a horizontal magnetic field. After the parts of the experimental facility are fabricated well and moved into the laboratory, the experiment station is assembled and tested on-site. At last, the experimental station is completed after the solid lithium is filled in and melted. Then, some experiments are conducted, including the lithium spreading performance on stainless-steel surface, the lithium film flow patterns under varying Reynolds numbers, and the MHD effects on the lithium film flow. The result shows that the liquid lithium film could spread well on the stainless steel which had been wetted by lithium sufficiently, and the horizontal magnetic field could steady the film flow pattern and restrain the surface wave of the film on the magnetic direction.     

Characterization of the three-dimensional supersonic flow for the MHD generator

A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the corner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.     

Saturated state of the nonlinear small-scale dynamo

We consider the problem of incompressible, forced, nonhelical, homogeneous, and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.     

Supersonic flow about a body exposed to electric and magnetic fields

The feasibility of using nonmechanical (electrogasdynamic, EGD, and magnetohydrodynamic, MHD) methods to control shock-wave configurations emerging in supersonic flows is investigated. In the EGD method, the flow is heated by a gas discharge; in the MHD one, the flow is influenced by a Lorentz force arising in a gas discharge upon applying a magnetic field. The influence of the gas discharge and MHD interaction on the position of a detached shock wave appearing in a supersonic xenon flow about a semicylindrical body is studied. A discharge is initiated in the immediate vicinity of the leading edge of the body, and the variation of the shock wave position with the intensity of the discharge (discharge current density) is traced when the influence of the EGD action increases and/or an external magnetic field is applied (the influence of the MHD action increases). Preliminary data for a supersonic air flow about a body are presented.     

Free convection effects and radiative heat transfer in MHD Stokes problem for the flow of dusty conducting fluid through porous medium

The present note deals with the effects of radiative heat transfer and free convection in MHD for a flow of an electrically conducting, incompressible, dusty viscous fluid past an impulsively started vertical non-conducting plate, under the influence of transversely applied magnetic field. The heat due to viscous dissipation and induced magnetic field is assumed to be negligible. The governing linear partial differential equations are solved by finite difference technique. The effects of various parameters (like radiation parameter N, Prandtl number Pr, porosity parameter K) entering into the MHD Stokes problem for flow of dusty conducting fluid have been examined on the temperature field and velocity profile for both the dusty fluid and dust particles.     

Hall effect on Hartmann flow and heat transfer of a Burgers' fluid

The effect of Hall current on the steady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers' fluid between two parallel electrically insulating infinite planes is studied. The MHD flow is generated by applying constant pressure gradient. An external uniform magnetic field normal to the disks is applied. The disks are kept at two different constant temperatures. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Reynolds number Re, Prandtl number Pr, Eckert number Ec, pressure gradient dp/dx and Hall parameter η are examined.     

Experimental investigation of magnetohydrodynamic action on a heat flux toward the surface of a model

Experimental data for magnetohydrodynamic (MHD) action on a supersonic nitrogen flow about an axisymmetric model are presented. The experiments were carried out in the Big Shock Tube (Ioffe Physical-Technical Institute), at the end of which a test section equipped with a supersonic nozzle was mounted. A test conic model coupled with a cylinder is attached to the output cross section of the nozzle. A magnetic field is produced by a solenoid placed on the cylindrical part of the model through which a pulsed current due to an external voltage source discharging passes. Electrodes on the conic part of the model initiate a gas discharge, which rotates about the axis of the model in the solenoidal magnetic field. The influence of the magnetic field on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface is investigated. Schlieren patterns of the flow about the model, photographic scans of the discharge glow, and heat flux measurements are taken. It is found that the magnetic field has an effect on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface. The dependence of MHD effects on the external voltage polarity is also revealed.     

高速飞行器磁控阻力特性

采用低磁雷诺数磁流体数学模型,对外加磁场下的高超声速半球体流场进行数值模拟.选取三种简单理想磁场(轴向、径向、周向均布磁场),分析了不同磁场类型对流场结构、气动阻力与洛伦兹阻力的影响及作用机理.研究发现,轴向磁场径向"挤压"效应使得激波外形凸出,且壁面静压存在"饱和现象";径向磁场存在轴向"外推"效应,较大的磁场强度会导致肩部形成高温区;周向磁场下感应电场的存在导致增阻效果很差.进而对比了两种相同驻点磁感应强度特殊分布磁场(偶极子磁场、螺线管磁场)下的流场,发现了不同于理想磁场的径向"扩张"效应.按增阻效果从大到小依次为径向磁场、螺线管磁场、轴向磁场、偶极子磁场、周向磁场.